The present invention relates to bipolar junction transistor (BJT) amplifiers, and more particularly to linearization bias circuit for BJT amplifiers that extends the compression point by keeping transconductance constant in the presence of varying input voltage amplitudes of an input radio frequency (RF) signal.
The 1 decibel (dB) compression point for a radio frequency (RF) bipolar junction transistor (BJT) amplifier has both an input and an output component. The output component results from the output power being limited, depending upon the load, either by voltage swing clipping or by the load current exceeding the DC collector current. The output limited compression point should be reasonably sharp. The input component of compression results from the exponential relationship between base-emitter voltage and collector current. As the peak of the AC component of the base-emitter voltage approaches the thermal voltage VT, the transconductance and input impedance of the BJT amplifier begin to drop off. These effects produce a gradual drop in gain which gives a softer compression point.
The key BJT relationships are now briefly discussed. The collector current ic of a BJT, when the base-emitter voltage VBE includes an AC term, is provided according to the following equations 1 and 2:                                                         i              C                        ≈                                          I                s                            ⁢                              exp                ⁡                                  (                                                            V                      BE                                                              V                      T                                                        )                                                              =                                    I              s                        ⁢                          exp              ⁡                              (                                                      V                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                                            V                    T                                                  )                                      ⁢                          exp              ⁡                              [                                                                            V                      P                                                              V                      T                                                        ⁢                                      cos                    ⁡                                          (                                              ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                            )                                                                      ]                                                    ⁢                  
                ⁢                              V            BE                    =                                    V                              D                ⁢                                  xe2x80x83                                ⁢                C                                      +                                          V                P                            ⁢                              cos                ⁡                                  (                                      ω                    ⁢                                          xe2x80x83                                        ⁢                    t                                    )                                                                                        (                  EQ          ⁢                      xe2x80x83                    ⁢          1                )                                                                                    i                C                            ≈                              xe2x80x83                            ⁢                                                i                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                  [                                                                            I                      0                                        ⁡                                          (                      x                      )                                                        +                                      2                    ⁢                                                                  I                        1                                            ⁡                                              (                        x                        )                                                              ⁢                                          cos                      ⁡                                              (                                                  ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                )                                                                              +                                      2                    ⁢                                                                  I                        2                                            ⁡                                              (                        x                        )                                                              ⁢                                          cos                      ⁡                                              (                                                  2                          ⁢                          ω                          ⁢                                                      xe2x80x83                                                    ⁢                          t                                                )                                                                              +                                                                                                                        xe2x80x83                            ⁢                                                2                  ⁢                                                            I                      3                                        ⁡                                          (                      x                      )                                                        ⁢                                      cos                    ⁡                                          (                                              3                        ⁢                        ω                        ⁢                                                  xe2x80x83                                                ⁢                        t                                            )                                                                      +                …                            ⁢                              xe2x80x83                            ]                                                          (                  EQ          ⁢                      xe2x80x83                    ⁢          2                )            
where Is is a constant describing the transfer characteristic of the BJT, xe2x80x9cexpxe2x80x9d denotes the exponential function (natural logarithm), VDC is the average DC applied base-emitter voltage, VP is the peak voltage of the input RF signal, xe2x80x9cCosxe2x80x9d denotes the cosine function, xcfx89 is the fundamental radian frequency of the input signal (xcfx89=2xcfx80f, where xe2x80x9cfxe2x80x9d is the fundamental frequency), xe2x80x9ctxe2x80x9d denotes time, iDC is the DC collector current due to the average DC applied base-emitter voltage VDC, xe2x80x9cxxe2x80x9d is the signal level of an input signal VIN normalized to the thermal voltage VT, and In(x) is the modified Bessel function of the first kind of order xe2x80x9cnxe2x80x9d.
The DC collector current iCDC and base current iBDC as well as the peak of the fundamental collector current iC(xcfx89) are provided in the following equation 3:                                           i                          C                              D                ⁢                                  xe2x80x83                                ⁢                C                                              =                                                    i                                  D                  ⁢                                      xe2x80x83                                    ⁢                  C                                            ⁢                                                I                  0                                ⁡                                  (                  x                  )                                            ⁢                              xe2x80x83                            ⁢                              i                                  B                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                                        =                                                            i                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                  ⁢                                                      I                    0                                    ⁡                                      (                    x                    )                                                              β                                      ⁢                  xe2x80x83                ⁢                  
                ⁢                                            i              C                        ⁡                          (              ω              )                                =                                                    i                                  D                  ⁢                                      xe2x80x83                                    ⁢                  C                                            ⁢              2              ⁢                                                I                  1                                ⁡                                  (                  x                  )                                            ⁢                              xe2x80x83                            ⁢                              i                                  D                  ⁢                                      xe2x80x83                                    ⁢                  C                                                      ≡                                          I                s                            ⁢                              exp                ⁡                                  (                                                            V                                              D                        ⁢                                                  xe2x80x83                                                ⁢                        C                                                                                    V                      T                                                        )                                                                                        (                  EQ          ⁢                      xe2x80x83                    ⁢          3                )            
where beta (xcex2) is the ratio of collector current to base current of the BJT. The zero order Bessel function I0(x) {modified of the first kind} is a scale factor for the DC that accounts for the increase due to rectification of the AC voltage applied to the base terminal of the BJT. Likewise the first order Bessel function I1(x) is a scale factor for the current at the fundamental frequency. The DC current iDC is defined as the collector current due to the average (DC) applied base-emitter voltage VDC.
The notation iDCN denotes the collector current due to the average base-emitter voltage of a particular transistor numbered xe2x80x9cNxe2x80x9d. Although iDC is not a function of the signal level x, the notation iDC(x) denotes the value of iDC forced by the bias circuit when a signal level x is applied to its base-emitter junction. Zero xe2x80x9c0xe2x80x9d will be substituted for xe2x80x9cxxe2x80x9d in the special case when no AC voltage is applied to the base-emitter junction.
A linear circuit has constant gain which means the transconductance gm should be constant and independent of signal level as indicated in the following equation 4:                               g          m                =                                                            i                C                            ⁡                              (                ω                )                                                    V              p                                =                                    (                                                i                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                                    V                  T                                            )                        ⁡                          [                                                2                  ⁢                                                            I                      1                                        ⁡                                          (                      x                      )                                                                      x                            ]                                                          (                  EQ          ⁢                      xe2x80x83                    ⁢          4                ]            
Many amplifiers are biased with constant base currents. For example, the base of the amplifier BJT is connected to a reference voltage through a larger value resistor or a current mirror. If the DC base current is constant, so is the DC collector current. For these currents to remain constant with increasing signal level, the DC base-emitter voltage must decrease as indicated by the following equations 5 and 6:                                                                         i                                  D                  ⁢                                      xe2x80x83                                    ⁢                  C                                            ⁡                              (                x                )                                      ⁢                                          I                0                            ⁡                              (                x                )                                              =                                                                      i                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                  ⁡                                  (                  0                  )                                            ⁢                                                I                  0                                ⁡                                  (                  0                  )                                                      =                                                                                i                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    0                    )                                                  →                                                      i                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    x                    )                                                              =                                                                    i                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    0                    )                                                                                        I                    0                                    ⁡                                      (                    x                    )                                                                                      ⁢                  
                ⁢                              Δ            ⁢                          xe2x80x83                        ⁢                          V                              D                ⁢                                  xe2x80x83                                ⁢                C                                              =                                    -                              V                T                                      ⁢                          ln              ⁡                              (                                                      I                    0                                    ⁡                                      (                    x                    )                                                  )                                                                        (                  EQ          ⁢                      xe2x80x83                    ⁢          5                )                                                      g            m                    ⁡                      (            x            )                          =                              [                                                            i                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                  ⁡                                  (                  0                  )                                                            V                T                                      ]                    ⁡                      [                                          2                ⁢                                                      I                    1                                    ⁡                                      (                    x                    )                                                                                                xI                  0                                ⁡                                  (                  x                  )                                                      ]                                              (                  EQ          ⁢                      xe2x80x83                    ⁢          6                )            
where xe2x80x9cInxe2x80x9d denotes that natural logarithm function. The transconductance decreases with increasing signal level starting for values of x of about one. A different bias condition is required for constant transconductance as indicated by the following equation 7:                               g          m                =                                            [                                                                    i                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    x                    )                                                                    V                  T                                            ]                        ⁡                          [                                                2                  ⁢                                                            I                      1                                        ⁡                                          (                      x                      )                                                                      x                            ]                                =                                                                                          i                                          D                      ⁢                                              xe2x80x83                                            ⁢                      C                                                        ⁡                                      (                    0                    )                                                                    V                  T                                            →                                                i                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                  ⁡                                  (                  x                  )                                                      =                                                            i                                      D                    ⁢                                          xe2x80x83                                        ⁢                    C                                                  ⁡                                  (                  0                  )                                            ⁡                              [                                  x                                      2                    ⁢                                                                  I                        1                                            ⁡                                              (                        x                        )                                                                                            ]                                                                        (                  EQ          ⁢                      xe2x80x83                    ⁢          7                )            
Usually RF BJT amplifier stages have biases which apply either a constant (i.e. DC) base current through an RF isolating resistor or constant base-emitter voltage through an isolating inductor. The base current is often generated by forcing a reference current through a current mirror. A base-emitter voltage bias is often generated by forcing the reference current through a similar BJT, possibly with a different emitter area.
It is desired to provide a bias control circuit for a BJT amplifier that establishes linear operation in the presence of varying input voltage amplitude of an input RF signal.
A linearization bias circuit for a bipolar junction transistor (BJT) amplifier according to an embodiment of the present invention includes a reference circuit, a current device and a transconductance amplifier. The BJT amplifier includes base, collector and emitter terminals in which the base terminal receives an input radio frequency (RF) signal. The reference circuit includes a reference terminal and a control terminal, where the control terminal is coupled to the base terminal of the BJT amplifier to control its operating point based on signal level of the RF signal. The current device provides a constant reference current to the reference terminal of the reference circuit, where the constant reference current has a level that is based on a desired collector current of the BJT amplifier. The transconductance amplifier has an input coupled to the reference terminal and an output coupled to the control terminal of the reference circuit, where the transconductance amplifier asserts its output to maintain the constant reference current into the reference terminal of the reference circuit. The reference circuit applies a predetermined relationship between DC and AC scale factors of collector current of the BJT amplifier. In this manner, the transconductance amplifier controls the base terminal to modify the operating point of the BJT amplifier to substantially maintain constant transconductance in the presence of varying input voltage amplitudes of the input RF signal.
The transconductance amplifier may be implemented as an emitter follower amplifier with an isolation resistor. The output of the transconductance amplifier may have a high impedance at a fundamental frequency of the RF signal, so that it is able to control the DC bias point without affecting the RF signal.
In one embodiment, the predetermined relationship is a linear regression according to an equation 2I1(x)/x=mI0(x)+b, where xe2x80x9cxxe2x80x9d is the normalized signal level of the RF signal, I0(x) is a zero order Bessel function representing a DC scale factor and I1(x) is a first order Bessel function representing an AC scale factor for current at a fundamental frequency of the RF signal. The values xe2x80x9cmxe2x80x9d and xe2x80x9cbxe2x80x9d are constants. In a specific embodiment to achieve desired linear operation, m is approximately 0.428 and b is approximately 0.592.
The reference circuit is implemented to substantially define the predetermined relationship to control the operating point in cooperation with the level of the reference current. One configuration of the reference circuit for implementing the relationship 2I1(x)/x=mI1(x)+b includes a sense BJT and a reference BJT. The sense BJT has a base terminal coupled to the base terminal of the BJT amplifier for receiving the input RF signal, a collector terminal coupled to the reference terminal and an emitter terminal for coupling to an emitter terminal of the BJT amplifier. The sense BJT may have an emitter area that is scaled down by a suitable scale factor relative to the emitter area of the BJT amplifier. The reference BJT has a base terminal, a collector terminal coupled to the reference terminal of the reference circuit and an emitter terminal coupled to the emitter terminal of the sense BJT. A low pass filter capacitor is coupled between the collector and emitter terminals of the sense and reference BJTs to remove AC. A low pass filter circuit is provided including a resistor coupled between the base terminals of the sense and reference BJTs and a capacitor coupled between the base and emitter terminals of the reference BJT. In this manner, the low pass filter circuit removes AC from the base terminal of the reference BJT. In a specific configuration, the constant reference current is approximately 2.34 times a desired collector current of the sense BJT, and the reference BJT has an emitter area that is approximately 1.38 times an emitter area of the sense BJT. It is noted that the constant reference current and the ratio of emitter areas of the sense and reference BJTs may be adjusted to account for circuit imperfections.
In another configuration, the predetermined relationship is according to an equation 2I1(x)/x=mI0(nx), where n is a predetermined value less than one, such as 0.73. In a specific configuration for implementing this relationship, the reference circuit includes a reference BJT, the low pass filter capacitor and an attenuation circuit. The reference BJT in this configuration may have an emitter area that is scaled down by a suitable scale factor relative to the BJT amplifier. The reference BJT in this case has a collector terminal coupled to the reference terminal of the reference circuit and an emitter terminal for coupling to an emitter terminal of the BJT amplifier. The low pass filter capacitor is coupled in a similar manner to remove AC from the collector terminal of the reference BJT. The attenuator circuit includes an attenuation resistor coupled between the bases of the reference and amplifier BJTs and an attenuation capacitor coupled between the base and emitter terminals of the reference BJT. The attenuator circuit applies a predetermined percentage of the level of the RF signal to the base terminal of the reference BJT at a fundamental frequency of the RF signal. In a particular embodiment to achieve substantial linearity, the predetermined percentage is approximately 73 percent (0.732). This configuration works for a limited frequency range.
The attenuation circuit may further include a second attenuation capacitor coupled in parallel with the attenuation resistor to expand the potential operable frequency ranges. In a specific configuration for a fundamental frequency f, a resistance R of the attenuation resistor, a capacitance C1 of the first attenuator capacitor, a capacitance C2 of the second attenuator capacitor, and a base to emitter capacitance Cxcfx80 of the reference BJT are such that the magnitude of (2xcfx80fRC2j+1)/(2xcfx80fR(C1+Cxcfx80+C2)+1) is approximately equal to the attenuation factor of 0.732.
A method of biasing a BJT amplifier according to an embodiment of the present invention includes providing the input RF signal to a bias control circuit, providing a constant reference current to the bias control circuit where the constant reference current has a level that is based on a desired DC collector current for the BJT amplifier, and controlling the base terminal of the BJT amplifier in order to substantially maintain constant transconductance of the BJT amplifier. In particular, the bias control circuit modifies the BJT amplifier operating point based on signal level of the input RF signal according to the predetermined relationship.
In one embodiment, the predetermined relationship is 2I1(x)/x=mI0(x)+b in a similar manner as previously described. In this case, the method may include scaling an emitter area of a reference BJT to be larger than an emitter area of a sense BJT by a predetermined scale factor, applying the input RF signal at the base terminal of the BJT amplifier to a base terminal of the sense BJT, low pass filtering the input RF signal as applied to the base terminal of the sense BJT to remove AC and providing the filtered RF signal to a base terminal of the reference BJT, scaling the constant reference current by a predetermined multiple of a desired DC collector current level of the sense BJT, applying the constant reference current to a reference node coupled to collector terminals of the sense and reference BJTs, low pass filtering AC from reference node, and controlling the DC level at the base terminal of the BJT amplifier using a transconductance amplifier. The transconductance amplifier forces a sum of collector currents of the sense and reference BJTs to be approximately the same as the constant reference current level. In one case, the predetermined scale factor is approximately 1.38 and the predetermined multiple is approximately 2.34.
Alternatively, the predetermined relationship is 2I1(x)/x=I0(nx) in which n is a constant, such as approximately 0.73. In this case, the method may include attenuating the input RF signal as applied to the base terminal of the sense BJT by a predetermined attenuation factor and providing the attenuated RF signal to a base terminal of a reference BJT, providing the constant reference current at a desired DC collector current level of the BJT amplifier, applying the constant reference current to a reference node coupled to a collector terminal of the reference BJT, low pass filtering AC from the reference node, and controlling DC at the base terminal of the BJT amplifier using a transconductance amplifier. The transconductance amplifier forces a collector current of the reference BJT to be approximately the same as the constant reference current level.